The flow separation state reflects the symmetry and stability of flow around spheres. The three-dimensional structures of flow around a rigid sphere at moderate Reynolds number (Re) between 20 and 400 by using finite volume method with adaptive mesh refinement are presented, and the process of separation angles changing from stable to oscillating state with increasing of Re is analyzed. The results show that the flow is steady, and the separation angles are stable and axisymmetric at Re in less than 200. The flow is unsteady and time-periodic, and the flow separation becomes regular fluctuations and asymmetric at Re = 300, which leads to the nonzero value of lateral force and the phase difference between lift and lateral force. At Re = 400, the flow is unsteady, non-periodic, and asymmetric, as is the flow separation. It’s concluded that the flow separation angle increases when Re increases within a range between 40 and 200. With Re continues to increase, the flow separation state changes from stable to periodically regular until quasi-periodically irregular. The vortex structure changes from no shedding to asymmetric periodic shedding, and finally to asymmetric and intermittently periodic vortex shedding. These results have important implications for the stability of flow around spheres.

Incompressible viscous flow past an ellipsoid of different aspect ratios ( ARs, the ratio of the vertical to the horizontal axis of the ellipsoid, is ranged from 0.5 to 2) at a Reynolds number of 300 is investigated numerically by a finite volume method with adaptive mesh refinement, and the effects of different aspect ratios on vortex shedding, flow separation, and drag coefficient are analyzed in detail. The accuracy of the present results is ascertained by comparing the present drag coefficient and Strouhal number with other literature studies. The results show that the Strouhal frequency of vortex shedding decreases and the magnitude of vortex shedding becomes weaker with an increase in the aspect ratio. In particular, a secondary frequency will occur within a certain interval of 0.8 ≤ AR ≤ 1.2. The vortex shedding appears as a hairpin vortex at AR ∈ [0.5, 1.6], whereas it becomes a double-line vortex at AR ≥ 1.8. Both the upper flow separation angle and the length of the separation bubble increase with an increase in the aspect ratio. The flow separation is symmetrical about the ( x, z)-plane only at 0.5 ≤ AR ≤ 0.7 and AR ≥ 1.8. Furthermore, the total drag coefficient and the pressure drag coefficient both increase gradually with an increase in the aspect ratio. Due to the trend of the contact area between the fluid and the surface of the ellipsoid, the friction drag coefficient decreases first ( AR ≤ 1) and then increases ( AR ≥1). The pressure drag coefficient reinforces the contribution to the total drag coefficient, and the contribution of the pressure drag coefficient grows with an increase in the aspect ratio.

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